Abstract

One of the key predictions of the nonlocal photopolymerization driven diffusion (NPDD) model is that a reduction in the extent of the nonlocal effects within a material will improve the high spatial frequency response. The NPDD model is generalized to more accurately model material absorbtivity. By eliminating the necessity for the steady-state approximation to describe the rate of change of monomer radical concentration, a more accurate physical representation of the initial transient behavior, at the start of grating growth, is achieved, which includes the effects of oxygen-based inhibition. The spatial frequency response of an acrylamide/polyvinylalcohol-based photopolymer is then improved through the addition of a chain transfer agent (CTA), sodium formate. Using the NPDD model demonstrates that the CTA has the effect of decreasing the average length of the polyacrylamide (PA) chains formed, thus reducing the nonlocal response parameter, σ. Further independent confirmation of the resulting reduction in the PA average molecular weight is provided using a diffusion-based holographic technique.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. M. R. Gleeson, J. V. Kelly, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 1-9 (2007).
    [Crossref]
  2. J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, “Adjusted intensity non-local diffusion model of photopolymer grating formation,” J. Opt. Soc. Am. B 19, 621-624 (2002).
    [Crossref]
  3. J. V. Kelly, F. T. O'Neill, and J. T. Sheridan, “Holographic photopolymer materials: non-local polymerization driven diffusion under non-ideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407-416 (2005).
    [Crossref]
  4. M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O'Neill, and J. T. Sheridan, “The effects of absorption and inhibition during grating formation in photopolymer materials,” J. Opt. Soc. Am. B 23, 2079-2088 (2006).
    [Crossref]
  5. J. T. Sheridan and J. R. Lawrence, “Non-local response diffusion model of holographic recording in photopolymer,” J. Opt. Soc. Am. A 17, 1108-1114 (2000).
    [Crossref]
  6. J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart) 112, 449-463 (2001).
    [Crossref]
  7. F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, “Comparison of holographic photopolymer materials by use of analytic non-local diffusion models,” Appl. Opt. 41, 845-852 (2002).
    [Crossref] [PubMed]
  8. L. Carretero, S. Blaya, R. Mallavia, R. Madrigal, A. Belendez, and A. Fimia, “Theoretical and experimental study of the bleaching of a dye in a film-polymerization process,” Appl. Opt. 37, 4496-4499 (1998).
    [Crossref]
  9. I. Aubrecht, M. Miller, and I. Koudela, “Recording of holographic gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth,” J. Mod. Opt. 45, 1465-1477 (1998).
    [Crossref]
  10. J. V. Kelly, M. R. Gleeson, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal analysis of grating formation in photopolymer using the non-local polymer driven diffusion model,” Opt. Express 13, 6990-7004 (2005).
    [Crossref] [PubMed]
  11. G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929-1939 (1994).
    [Crossref]
  12. S. Piazolla and B. K. Jenkins, “First-harmonic diffusion model for holographic grating formation in photopolymers,” J. Opt. Soc. Am. B 17, 1147-1157 (2000).
    [Crossref]
  13. M. Pabon, J. Selb, F. Candau, and R. G. Gilbert, “Polymerization of acrlyamide in solution and inverse emulsion: number molecular weight distribution with chain transfer agent,” Polymer 40, 3101-3106 (1999).
    [Crossref]
  14. M. Fevola, R. Hester, and C. McCormack, “Molecular weight control of polyacyrlamide with sodium formate as a chain-transfer agent: characterization via size exclusion chromatography/multi-angle laser light scattering and determination of chain-transfer constant,” J. Polym. Sci., Part A: Polym. Chem. 41, 560-568 (2003).
    [Crossref]
  15. L. A. Goretta and R. R. Otremba, Formic acid alkali metal formates as chain transfer agents in the preparation of acrylamide polymers, U.S. patent 4,307,215 (December 22, 1981).
  16. H. A. Gartner, Process for the production of high molecular weight copolymers of diallyammonium monomers and acrylamide monomers in an aqueous dispersed phase, U.S. patent 5,171,783 (December 15, 1992).
  17. M. C. Cole, F. R. Askham, and W. L. Wilson, “Holographic recording medium with control of photopolymerization and dark reaction,” U.S. patent 2006/0194120 A1 (August 31, 2006).
  18. F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, “Improvement of holographic recording material using aerosol sealant,” J. Opt. A, Pure Appl. Opt. 3, 20-25 (2001).
    [Crossref]
  19. M. R. Gleeson, J. V. Kelly, F. T. O'Neill, and J. T. Sheridan, “Recording beam modulation during grating formation,” Appl. Opt. 44, 5475-5482 (2005).
    [Crossref] [PubMed]
  20. P. W. Atkins, Physical Chemistry, 4th ed. (Oxford U. Press, 1992).
  21. J. Crank, The Mathematics of Diffusion, 2nd ed. (Oxford U. Press, 1975).
  22. H. Kogelnik, “Coupled wave theory for thick holographic gratings,” Bell Syst. Tech. J. 48, 2909-2947 (1969).
  23. J. Crank and G. S. Park, Diffusion in Polymers, 1st ed. (Academic, 1968).
  24. S. Gallego, M. Ortuno, C. Niepp, A. Marquez, A. Belendez, and I. Pascual, “Characterization of polyvinyl alcohol/acrylamide holographic memories with a first-harmonic diffusion model,” Appl. Opt. 44, 6205-6210 (2005).
    [Crossref] [PubMed]
  25. D. J. Lougnot and C. Turk, “Photopolymers for holographic recording: II. Self-developing materials for real-time interferometry,” Pure Appl. Opt. 1, 251-268 (1992).
    [Crossref]
  26. D. J. Lougnot and C. Turk, “Photopolymers for holographic recording: III. Time modulated illumination and thermal post-effect,” Pure Appl. Opt. 1, 269-279 (1992).
    [Crossref]
  27. A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amat-Guerri, “Elimination of oxygen inhibition in photopolymer systems used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
    [Crossref]
  28. A. K. O'Brien and C. N. Bowman, “Modelling the effect of oxygen on photopolymerization kinetics,” Macromol. Theory Simul. 15, 176-182 (2006).
    [Crossref]
  29. G. Odian, Principles of Polymerization (Wiley, 1991).
  30. H. Inaba and H. Naito, “Measurement of the refractive indices of lithium-sodium formate and sodium formate crystals,” Opto-electronics (London) 5, 551-555 (1973).
    [Crossref]
  31. S. Wu and E. N. Glytsis, “Holographic grating formation in photopolymers: analysis and experimental results based on a nonlocal diffusion model and rigorous coupled-wave analysis,” J. Opt. Soc. Am. B 20, 1177-1188 (2003).
    [Crossref]
  32. C. E. Close, M. R. Gleeson, F. T. O'Neill, J. V. Kelly, and J. T. Sheridan, “Control and measurement of the physical properties in acrylamide based photopolymer materials,” Proc. SPIE 5827, 346-357 (2005).
    [Crossref]
  33. S. Gallego, M. Ortuno, C. Niepp, A. Marquez, A. Belendez, J. V. Kelly, and J. T. Sheridan, “3 Dimensional analysis of holographic photopolymers based memories,” Opt. Express 13, 3543-3557 (2005).
    [Crossref] [PubMed]

2007 (1)

M. R. Gleeson, J. V. Kelly, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 1-9 (2007).
[Crossref]

2006 (2)

2005 (6)

2003 (2)

M. Fevola, R. Hester, and C. McCormack, “Molecular weight control of polyacyrlamide with sodium formate as a chain-transfer agent: characterization via size exclusion chromatography/multi-angle laser light scattering and determination of chain-transfer constant,” J. Polym. Sci., Part A: Polym. Chem. 41, 560-568 (2003).
[Crossref]

S. Wu and E. N. Glytsis, “Holographic grating formation in photopolymers: analysis and experimental results based on a nonlocal diffusion model and rigorous coupled-wave analysis,” J. Opt. Soc. Am. B 20, 1177-1188 (2003).
[Crossref]

2002 (2)

2001 (2)

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart) 112, 449-463 (2001).
[Crossref]

F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, “Improvement of holographic recording material using aerosol sealant,” J. Opt. A, Pure Appl. Opt. 3, 20-25 (2001).
[Crossref]

2000 (2)

1999 (1)

M. Pabon, J. Selb, F. Candau, and R. G. Gilbert, “Polymerization of acrlyamide in solution and inverse emulsion: number molecular weight distribution with chain transfer agent,” Polymer 40, 3101-3106 (1999).
[Crossref]

1998 (2)

L. Carretero, S. Blaya, R. Mallavia, R. Madrigal, A. Belendez, and A. Fimia, “Theoretical and experimental study of the bleaching of a dye in a film-polymerization process,” Appl. Opt. 37, 4496-4499 (1998).
[Crossref]

I. Aubrecht, M. Miller, and I. Koudela, “Recording of holographic gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth,” J. Mod. Opt. 45, 1465-1477 (1998).
[Crossref]

1994 (1)

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929-1939 (1994).
[Crossref]

1993 (1)

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amat-Guerri, “Elimination of oxygen inhibition in photopolymer systems used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[Crossref]

1992 (2)

D. J. Lougnot and C. Turk, “Photopolymers for holographic recording: II. Self-developing materials for real-time interferometry,” Pure Appl. Opt. 1, 251-268 (1992).
[Crossref]

D. J. Lougnot and C. Turk, “Photopolymers for holographic recording: III. Time modulated illumination and thermal post-effect,” Pure Appl. Opt. 1, 269-279 (1992).
[Crossref]

1973 (1)

H. Inaba and H. Naito, “Measurement of the refractive indices of lithium-sodium formate and sodium formate crystals,” Opto-electronics (London) 5, 551-555 (1973).
[Crossref]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick holographic gratings,” Bell Syst. Tech. J. 48, 2909-2947 (1969).

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick holographic gratings,” Bell Syst. Tech. J. 48, 2909-2947 (1969).

J. Appl. Phys. (1)

M. R. Gleeson, J. V. Kelly, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 1-9 (2007).
[Crossref]

J. Mod. Opt. (3)

I. Aubrecht, M. Miller, and I. Koudela, “Recording of holographic gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth,” J. Mod. Opt. 45, 1465-1477 (1998).
[Crossref]

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929-1939 (1994).
[Crossref]

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amat-Guerri, “Elimination of oxygen inhibition in photopolymer systems used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, “Improvement of holographic recording material using aerosol sealant,” J. Opt. A, Pure Appl. Opt. 3, 20-25 (2001).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (5)

J. Polym. Sci., Part A: Polym. Chem. (1)

M. Fevola, R. Hester, and C. McCormack, “Molecular weight control of polyacyrlamide with sodium formate as a chain-transfer agent: characterization via size exclusion chromatography/multi-angle laser light scattering and determination of chain-transfer constant,” J. Polym. Sci., Part A: Polym. Chem. 41, 560-568 (2003).
[Crossref]

Macromol. Theory Simul. (1)

A. K. O'Brien and C. N. Bowman, “Modelling the effect of oxygen on photopolymerization kinetics,” Macromol. Theory Simul. 15, 176-182 (2006).
[Crossref]

Opt. Express (2)

Optik (Stuttgart) (1)

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart) 112, 449-463 (2001).
[Crossref]

Opto-electronics (London) (1)

H. Inaba and H. Naito, “Measurement of the refractive indices of lithium-sodium formate and sodium formate crystals,” Opto-electronics (London) 5, 551-555 (1973).
[Crossref]

Polymer (1)

M. Pabon, J. Selb, F. Candau, and R. G. Gilbert, “Polymerization of acrlyamide in solution and inverse emulsion: number molecular weight distribution with chain transfer agent,” Polymer 40, 3101-3106 (1999).
[Crossref]

Proc. SPIE (1)

C. E. Close, M. R. Gleeson, F. T. O'Neill, J. V. Kelly, and J. T. Sheridan, “Control and measurement of the physical properties in acrylamide based photopolymer materials,” Proc. SPIE 5827, 346-357 (2005).
[Crossref]

Pure Appl. Opt. (2)

D. J. Lougnot and C. Turk, “Photopolymers for holographic recording: II. Self-developing materials for real-time interferometry,” Pure Appl. Opt. 1, 251-268 (1992).
[Crossref]

D. J. Lougnot and C. Turk, “Photopolymers for holographic recording: III. Time modulated illumination and thermal post-effect,” Pure Appl. Opt. 1, 269-279 (1992).
[Crossref]

Other (7)

G. Odian, Principles of Polymerization (Wiley, 1991).

J. Crank and G. S. Park, Diffusion in Polymers, 1st ed. (Academic, 1968).

P. W. Atkins, Physical Chemistry, 4th ed. (Oxford U. Press, 1992).

J. Crank, The Mathematics of Diffusion, 2nd ed. (Oxford U. Press, 1975).

L. A. Goretta and R. R. Otremba, Formic acid alkali metal formates as chain transfer agents in the preparation of acrylamide polymers, U.S. patent 4,307,215 (December 22, 1981).

H. A. Gartner, Process for the production of high molecular weight copolymers of diallyammonium monomers and acrylamide monomers in an aqueous dispersed phase, U.S. patent 5,171,783 (December 15, 1992).

M. C. Cole, F. R. Askham, and W. L. Wilson, “Holographic recording medium with control of photopolymerization and dark reaction,” U.S. patent 2006/0194120 A1 (August 31, 2006).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Postexposure decay curves for cases 1, 2, and 3.

Fig. 2
Fig. 2

Simulation of the rate of change of inhibitor concentration with time for three different inhibition rate constants, k z [ cm 3 mol s ] : 8 × 10 8 (small dashed curve); 1 × 10 9 (solid curve); 6 × 10 9 (large dashed curve).

Fig. 3
Fig. 3

Simulation of the change in polymerization rate during exposure for three different propagation rates, k p [ cm 3 mol s ] : 3 × 10 7 (small dashed curve); 4 × 10 7 (solid curve); 5 × 10 7 (large dashed curve).

Fig. 4
Fig. 4

Experimental growth curve data and fits at 2750 lines mm . Standard material (solid curve); with CTA (dashed curve).

Tables (6)

Tables Icon

Table 1 Rates of Polymer Diffusion Extracted from Fig. 1 for Cases 1, 2, and 3

Tables Icon

Table 2 Parameters Extracted from Fits to Experimentally Obtained Transmission Curves

Tables Icon

Table 3 Components and Volume Fractions of the Material Makeup

Tables Icon

Table 4 Measured Refractive Index Values of the Material Components

Tables Icon

Table 5 Spatial Frequency Parameter Estimations for Standard AA/PVA Material Layer

Tables Icon

Table 6 Parameter Estimations for Spatial Frequencies in AA/PVA and CTA Material

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

R ( x , x ) = 1 2 π σ exp [ ( x x ) 2 2 σ ] ,
n 1 ( t ) = λ sin 1 η ( t ) cos θ B π d ,
n 1 ( t ) = n 1 ( t ) + Δ n 1 exp [ α PA t ] .
ln [ n 1 ( t ) n 1 ( t final ) ] = + ln [ Δ n 1 ] α PA t .
d C ( x , t ) d t = D PA d 2 C ( x , t ) d x 2 ,
C ( x , 0 ) = C AV + C a cos [ K x ] ,
C ( x , t ) = C AV + C a exp { D P A K 2 t } cos [ K x ] .
Δ n 1 exp { α PA t } C a exp { D PA K 2 t } ,
α PA = D PA K 2 .
d A ( t ) d t = ϕ I a ( t ) + k r [ A 0 A ( t ) ] ,
I a ( t ) = I 0 { 1 exp [ ε A ( t ) d ] } d ,
I 0 = I i ( λ N a h c ) T s f ,
A ( t ) = 1 ε d ln { 1 + [ exp ( ε d A 0 ) 1 ] exp ( ε ϕ I 0 t ) } .
I a ( t ) = I 0 d { [ exp ( ε d A 0 ) 1 ] exp ( ε ϕ I 0 t ) 1 + [ exp ( ε d A 0 ) 1 ] exp ( ε ϕ I 0 t ) } .
I 0 = I a ( t ) + I T ( t ) .
T ( t ) = T s f 1 + [ exp ( ε d A 0 ) 1 ] exp ( ε ϕ I 0 t ) .
R p d [ M ] d t = k p [ M . ] [ M ] ,
d [ M . ] d t = R i 2 k t [ M . ] 2 k z [ Z ] [ M . ] = 0 ,
R p = k p [ M ] 4 k t { 8 k t R i + k z 2 [ Z ] 2 k z [ Z ] } .
Z ( x , t ) t = x [ D z ( x , t ) Z ( x , t ) x ] k z Z ( x , t ) M . ( x , t ) ,
M . ( x , t ) t = R i 2 k t [ M . ( x , t ) ] 2 k z Z ( x , t ) M . ( x , t ) .
Z ( t ) t = k z Z ( t ) M . ( t ) ,
M . ( t ) t = R i 2 k t [ M . ( t ) ] 2 k z Z ( t ) M . ( t ) .
R i = 2 ϕ I a ( t ) ,
F ( x , t ) = F 0 ( t ) [ 1 + V cos ( K x ) ] .
F 0 ( t ) = k p M . ( t ) .
u ( x , t ) t = x [ D ( x , t ) u ( x , t ) x ] + 0 t R ( x , x ; t , t ) F ( x , t ) [ u ( x , t ) ] β d t d x ,
d u 0 ( t ) d t = F 0 u 0 ( t ) 1 2 F 0 V u 1 ( t ) ,
d u 1 ( t ) d t = S 1 F 0 V u 0 ( t ) [ S 1 F 0 + D 0 K 2 exp ( α F 0 t ) cosh ( α F 0 V t ) ] u 1 ( t ) [ S 1 2 F 0 V D 0 K 2 exp ( α F 0 t ) sinh ( α F 0 V t ) ] u 2 ( t ) ,
N ( x , t ) = 0 t + R ( x x ) F ( x , t ) u ( x , t ) d x d t ,
N 1 ( t ) = S 0 t F 0 [ V u 0 ( t ) + u 1 ( t ) + 1 2 V u 2 ( t ) ] d t .
n 2 1 n 2 + 2 = ϕ ( AA ) n AA 2 1 n AA 2 + 2 + ϕ ( PVA ) n PVA 2 1 n PVA 2 + 2 + ϕ ( BA ) n BA 2 1 n BA 2 + 2 + ϕ ( TEA ) n TEA 2 1 n TEA 2 + 2 + ( ϕ ( CTA ) n CTA 2 1 n CTA 2 + 2 ) ,
ϕ ( AA ) + ϕ ( PVA ) + ϕ ( BA ) + ϕ ( TEA ) + ϕ ( CTA ) = 1 .

Metrics